Sentence examples for problem under boundary from inspiring English sources

We also approximate solution of this problem under boundary condition (mathbf{S_{2}}).

We solve the problem under boundary condition (S_{2}) and the results are displayed in Table 3.

On solving the problem under boundary conditions (S_{2}) we observe that the method provides very accurate estimate of solution.

We simulate the proposed algorithm to solve this problem under boundary conditions (S_{1}) and we observe that the method works well.

Wang and Sun [2] and Luo and Gao [3] applied the Schauder fixed point theorem to show the existence of positive solutions of a fourth-order dynamic boundary value problem under different boundary value conditions.

In this paper, our target is to construct a box-type difference scheme with (O tau^{2}+h^{2})) accuracy for that problem under Neumann boundary conditions.

The given problem is solved on the superposition of two auxiliary problems under different boundary conditions.

Some authors have discussed the global and blow-up solutions of parabolic problems under Robin boundary conditions and have got a lot of meaningful results (see [14 20] and the references cited therein).

They determine, for solutions that blow up, a lower bound for the blow-up time t ∗ in a bounded domain Ω ⊂ R N for N = 3. Besides, some authors have also started to consider the blow-up phenomena of those problems under Robin boundary conditions (see [17] [19]).

We solve this problem with the proposed method under boundary conditions (S_{1}), and we observe that the approximate solution obtained via the new method is very accurate even for very small value of N. Figure 4(a) shows the comparison of the approximate solution with the exact solution.

To define this method we apply invariance properties of Newton's free boundary problem under a scaling group of point transformations.